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The duality between the anti-exchange closure operators and the path independent choice operators on a finite set

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Author Info
Bernard Monjardet () (CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - CNRS : UMR8095 - Université Panthéon-Sorbonne - Paris I)
Raderanirina Vololonirina (CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - CNRS : UMR8095 - Université Panthéon-Sorbonne - Paris I)

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Abstract

In this paper, we show that the correspondence discovered by Koshevoy ([18]) and Johnson and Dean ([15],[16]) between anti-exchange closure operators and path independent choice operators is a duality between two semilattices of such operators. Then we use this duality to obtain results concerning the "ordinal" representations of path independent choice functions from the theory of anti-exchange closure operators.

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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00214289_v1.

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Date of creation: 2001
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Publication status: Published, Mathematical Social Sciences, 2001, 41, 2, 131-150
Handle: RePEc:hal:cesptp:halshs-00214289_v1

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Keywords: Anti-exchange closure operator; choice function; convex geometry; path independence; partial order; semilattice.;

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  1. Bernard Monjardet, 2007. "Some order dualities in logic, games and choices," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00202326_v1, HAL. [Downloadable!]
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